Describe how to determine the intercepts of rational function?
[tex]\large \: \: \: \: \: \: ➢[/tex]To find the intercepts replace 0 for x and solve y of x after that. To find the intercepts the point where the graph crosses the x-axis "also known as zeros, substitute 0 for y and solve for x.
Example:
[tex]\large \: ➢[/tex]Find the intercepts of the function given.
[tex] \: \: \: \: \: \: \large\tt f(x) = \frac{ \: \: x + 10 \: \: }{x - 5} [/tex]
[tex]\large \: ➢[/tex]To find the y-intercept, we must substitute in 0 for each x:
[tex] \: \: \: \: \: \: \large \tt \: f(x) = \frac{ \: \: 0 + 10 \: \: }{0 - 5} [/tex]
[tex]\large \: ➢[/tex]And then simplify:
[tex] \: \: \: \: \: \: \large \tt f(x) = \frac{ \: \: 10 \: \: }{ - 5} [/tex]
[tex]\: \: \: \: \: \: \large \tt f(x) = \: - 2[/tex]
[tex]\large \: ➢[/tex]There is a y-intercept at ( 0.2 ). (Notice that 0 is the x coordinate because on the y-axis, x = 0.)
[tex]\large \: ➢[/tex]To find the x-intercept, we must substitute in 0 for y or f(x):
[tex] \: \: \: \: \: \: \large \tt 0 = \frac{ \: \: x + 10 \: \: }{x - 5} [/tex]
[tex] \: \: \: \: \: \: \large \tt0(x - 5) = x + 10[/tex]
[tex] \: \: \: \: \: \: \large \tt0 = x + 10[/tex]
[tex] \: \: \: \: \: \: \large \tt x = - 10[/tex]
[tex]\large \: ➢[/tex]There is a y-intercept at ( -10,0 ). (Notice that 0 is the y coordinate because on the x-axis, y = 0.)
Note:
[tex]\large \: ➢[/tex]Not all rational functions have both an x or y intercept. If you cannot find a real solution, then it does not have that intercept.
#CarryOnLearning
